Sign up for a giveaway account during StatCounter as well as follow a 'Install Code' wizard to generate your StatCounter code.
When prompted, make sure to choose Blogger / Blogspot as your Blog/Web Page Editor from a drop down list.
Copy a StatCounter code.
Log in to your Blogger / Blogspot blog.
Go to a blueprint area.

Click a single of a Add a Gadget links during a bottom or to a right of your blog blueprint area (as indicated in a picture). (Note from a screenshot which we are in a Page Elements tab of a Layout area.)

Clicking Add a Gadget opens a new window similar to a a single pictured below.

Scroll down by a list of Basic gadgets to find a HTML/Javascript tool as shown in a design below. Click a content (that says HTML/JavaScript) to supplement a tool to your blog.

Paste a StatCounter code in to a content territory of a gadget.
Click "Save" as well as that's it!